Gyrokinetic limit of the 2D Hartree equation in a large magnetic field

2024/03/28 by Denis Périce, Périce, Denis, Nicolas Rougerie +1
Physics and Astronomy · #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena

paper · pdf · doi:10.48550/arxiv.2403.19226

openalex created_date 2024/03/28 · openalex publication_date 2024/03/28 · openalex updated_date 2026/07/28

Abstract

We study the dynamics of two-dimensional interacting fermions submitted to a homogeneous transverse magnetic field. We consider a large magnetic field regime, with the gap between Landau levels set to the same order as that of potential energy contributions. Within the mean-field approximation, i.e. starting from Hartree's equation for the first reduced density matrix, we derive a drift equation for the particle density. We use vortex coherent states and the associated Husimi function to define a semi-classical density almost satisfying the limiting equation. We then deduce convergence of the density of the true Hartree solution by a Dobrushin-type stability estimate.

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